Two parallel resistanceless rails are connected by an inductor of inductance `L` at one end as shows in Fig. A magnetic field `B` exists in the space which is perpendicular to the plane of the rails. Now a conductor of length `l` and mass `m` is placed transverse on the rail and given an impulse `J` toward the rightward direction. Then choose the correct option (s).

Options

A. Velocity of the conductor is half of the initial velocity after a displacement of the conductor
`d = sqrt((3J^(2)L)/(4B^(2)l^(2)m))`
B. Velocity of the conductor is half of the initial velocity after a displacement of the conductor
`d = sqrt((3J^(2)L)/(B^(2)l^(2)m))`
C. Current flowing trough the inductor at the instant when velocity of the conductor is half of the initial velocity `i = sqrt((3 J^(2))/(4Lm))`
D. Current flowing trough the inductor at the instant when velocity of the conductor is half of the initial velocity `i = sqrt((3 J^(2))/(Lm))`

Answer

A, C